We extend Reichel-Jacobs coalgebraic account of objects and classes in
Object Oriented Programming to include \emph{generalized binary methods},
i.e. methods which take more than one parameter of a class type.
Furthermore, in order to take care of class \emph{constructors}, we model classes
as \emph{bialgebras}, i.e. we introduce also an {\em algebra part} in
our description of a class. 
We  show how  generalized binary methods can be modelled 
in the coalgebraic setting using purely \emph{covariant functors}. 
Class parameters of generalized binary methods include (possibly infinite) products, sums,
powerset and  relational type constructors. The latter arises when we consider functions as 
\emph{graphs}.
We propose two solutions for modeling generalized binary methods. 
In the first solution, we reduce  the behaviour of a generalized binary method to that of a
bunch of unary methods. These are obtained by \emph{freezing} 
the types of the extra class parameters to constant types.
These methods can then be modelled by standard (covariant) 
coalgebraic tools.
Alternatively, we propose to treat binary methods
as {\em graphs} instead of functions, thus turning contravariant
occurrences in the functor into covariant ones. 
We study and compare these two approaches.